The use of fake accents by actors is a long-held tradition. Even though the accents are not real, they can help the audience get more involved in movies. Just as special effects, sets, and music enhance movies, fake accents are just one more thing that make movies interesting to watch.
People are so in love with the idea of the "good old days" that they lead themselves to believe that an accent like Cary Grant's can make a movie better. If anything, that non-existent accent can only heighten the artificiality of those old movies and make them less easy to enjoy.
Mid-Atlantic English did not being more richness to movies, especially when watching them in the 21st century. For example, the Sound of Music- these people were supposed to be Austrian yet sound American, or wait are they British? I don't believe for a second that they were within 1000 miles of a Nazi. It's extremely unrealistic.
Mid-Atlantic English is an artificial creation for movies. It adds no more richness to the experience than a cartoon drawing to represent an action scene. I actually think it takes away from the movies; fake accents feel so out of place that they constantly interrupt the flow of the movie.